Question

Suppose that you have received 100 email messages 90 of which
are genuine and

10 are spam. Suppose that your email server runs a spam filtering
software that

classified the above email messages as follows.

• Out of the the 90 genuine messages 88 classified as genuine but 2
are wrongly

flagged as spam.

• The probability of correct classification of a message is at
least 97%

Using the above data, please answer the three questions below. Each
answer must

be accompanied with an explanation as to why you believe the answer
to be correct.

A correct answer only (without the explanation) will be worth 1
point for part a),

2 points for part b), and 2 points for part c). Explanation only
without an explicit

answer will not be awarded any marks.

(a) | What is largest possible number of spam messages (out of 10) that the software |

can incorrectly classify as genuine? | . |

(b) | What is the smallest possible probability that the spam filter flags an email |

message as spam provided that the message is indeed a spam? | |

(c) | What is the smallest probability that an email message is spam provided that |

it is flagged as spam by the spam filter? | (8 marks |

Answer #1

**Solution:**

a) Considering the lowest probability of correct classification
be 97%, so out of 100 messages at max 3 can be classified as wrong,
and already out of the 90 genuine messages two are wrongly
classified, so only 1 can be classified inaccurately for spam
messages, meaning 1 out of the 10. **So the largest number of
spam messages that can be incorrectly classify as genuine is
1.**

b) Smalles probability of reading the spam as spam, means
highest probability of making a mistake with the spam emails, that
is 1/10 = 10% chance of being wrong, while **90% chance of
guessing the spam as indeed a spam.**

**c)** The system flagged 2 correct messages as
spam as well, and 9 spam messages as spam, so smallest probability
will be = 9/11 = 0.81818 = **81.82% Answer**

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